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We introduce a novel approach to sample the canonical ensemble at constant temperature and applied electric potential. Our approach can be straightforwardly implemented into any density-functional theory code. Using thermopotentiostat…
We consider numerical approximations of stochastic differential equations by the Euler method. In the case where the SDE is elliptic or hypoelliptic, we show a weak backward error analysis result in the sense that the generator associated…
We introduce and analyze a post-processing for a family of variational space-time approximations to wave problems. The discretization in space and time is based on continuous finite element methods. The post-processing lifts the fully…
We describe a proof-of-concept development and application of a phase averaging technique to the nonlinear rotating shallow water equations on the sphere, discretised using compatible finite element methods. Phase averaging consists of…
We propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear…
We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value…
We introduce a family of fourth order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. Each method in the family may be viewed as a correction of a linear two-step method, where the correction…
We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the…
We investigate numerically a quasi-static elasticity system of Kachanov-type. To do so we propose an Euler time discretization combined with a suitable finite elements scheme (FEM) to handle the discretization is space. We use ODE-type…
The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion-convection-reaction equations and boundary conditions of mixed type. Since neither conformity…
We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…
This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…
In this article, we consider a one-dimensional Timoshenko system subject to different types of dissipation (linear and nonlinear dampings). Based on a combination between the finite element and the finite difference methods, we design a…
In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve…
We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…
We analyze fully implicit and linearly implicit backward difference formula (BDF) methods for quasilinear parabolic equations, without making any assumptions on the growth or decay of the coefficient functions. We combine maximal parabolic…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…
We investigate the potential of numerical algorithms to decipher the kinetic parameters involved in multi-step chemical reactions. To this end we study a dimerization kinetics of protein as a model system. We follow the dimerization…
Generation of equilibrium configurations is the major obstacle for numerical investigation of the slow dynamics in supercooled liquid states. The parallel tempering (PT) technique, originally proposed for the numerical equilibration of…